The invention relates to a method of forming high precision through holes in workpieces with a laser beam. In particular, the invention relates to forming injection holes in fuel injection nozzles. European patent EP-A 02 99 143 discloses a method of and apparatus for producing hole having a small diameter in injection nozzles. According to the method disclosed in EP-A 02 99 143, initially a hole with a diameter which is less than the nominal diameter of the injection hole is formed with laser beam. Then, the smaller diameter hole is brought to the nominal diameter by using an electrical discharge drilling. To this end, a wire electrode is inserted into the smaller diameter hole and brings the hole diameter to a predetermined value by removing the material with spark erosion. An annular space between the outer diameter of the electrode and the hole wall is flushed with an electrolyte that carries away the eroded material particles. Thereby a smooth high precision cylindrical hole is produced. However, with this method, the hole wall must be sufficiently thick to be able to withstand loads acting thereon, i.e., pressure.